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Question
Simplify : `("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)`
Solution
`("i"^592 + "i"^590 + "i"^588 + "i"^586 + "i"^584)/("i"^582 + "i"^580 + "i"^578 + "i"^576 + "i"^574)`
= `("i"^584 ("i"^8 + "i"^6 + "i"^4 + "i"^2 + 1))/("i"^574 ("i"^8 + "i"^6 + "i"^4 + "i"^2 + 1))`
= `("i"^584)/("i"^574)`
= i10
= (i2)5
= (–1)5
= – 1.
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